Aims: By studying the photospheric abundances of 4 RV Tauri stars in the LMC, we test whether the depletion pattern of refractory elements, seen in similar Galactic sources, is also common for extragalactic sources. Since this depletion process probably only occurs through interaction with a stable disc, we investigate the circumstellar environment of these sources. Methods: A detailed photospheric abundance study was performed using high-resolution UVES optical spectra. To study the circumstellar environment we use photometric data to construct the spectral energy distributions of the stars, and determine the geometry of the circumstellar environment, whereas low-resolution Spitzer-IRS infrared spectra are used to trace its mineralogy. Results: Our results show that, also in the LMC, the photospheres of RV Tauri stars are commonly affected by the depletion process, although it can differ significantly in strength from source to source. From our detailed disc modelling and mineralogy study, we find that this process, as in the Galaxy, appears closely related to the presence of a stable Keplerian disc. The newly studied extragalactic objects have similar observational characteristics as Galactic post-AGB binaries surrounded by a dusty disc, and are therefore also believed to be part of a binary system. One source shows a very small infrared excess, atypical for a disc source, but still has evidence for depletion. We speculate this could point to the presence of a very evolved disc, similar to debris discs seen around young stellar objects.